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Quadratic Equations

Class 10 Mathematics के इस tag से जुड़े questions। हर question के साथ chapter, topic, level और difficulty दी गई है।

MathematicsGiven that \\(\alpha\ne -1\\), what condition on \\(\alpha\\) is necessary for the equation \\((\alpha+1)x^2-2\alpha x+\alpha=0\\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor which values of \(\lambda\) does the equation \(x^2-2\lambda x+\lambda=0\) have equal roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf (x^2-2\lambda x+\lambda=0) has two real and distinct roots, which condition on (\lambda) is correct?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhich root nature is correct for 2x² − 5√2x + 12 = 0?Class 10Quadratic EquationsNature of RootsLevel 37HardMathematicsWhat is the nature of the roots of the quadratic equation \(3x^2-2\sqrt{6}x+2=0\)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhich quadratic equation has real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf \(a\) and \(b\) are real numbers, which of the following relations is necessary for the equation \(x^2-2(a+b)x+(a^2+b^2)=0\) to have real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor real numbers a and b, if the equation \(x^2-2(a+b)x+(a-b)^2=0\) has real and distinct roots, which condition on a and b is correct?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhich condition is correct for real roots of ((k-2)x^2+2kx+(k+3)=0), if (k\neq2)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIn ((k-2)x^2+2kx+(k+3)=0), with (k\neq2), what is the correct condition for real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf \(k\neq 0\) and \(kx^2-2(k+1)x+(k+3)=0\) is a quadratic equation, what must be the value of \(k\) for it to have equal roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf \(k\) is a real number, what is the correct condition for the equation \(x^2+2(k-1)x+(k+5)=0\) to have no real roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf (x^2+2(k-1)x+(k+5)=0) has no real roots, in which interval will (k) lie?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor which value of \(k\) will the two roots of the quadratic equation \(2x^2-(k+4)x+2k=0\) be equal?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor what value of \(k\) will the quadratic equation \(2x^2-(k+4)x+2k=0\) have equal roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsFor the equation \((p+1)x^2-2(p+2)x+(p+4)=0\), where \(p\ne -1\), what condition on \(p\) ensures that the roots are real?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhat condition on \(m\) is necessary for the equation \(x^2-(m+3)x+3m=0\) to have two real and distinct roots?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsIf \(k\) is a real number and the roots of the equation \(x^2-2(k+1)x+(k^2+4)=0\) are real, what is the correct condition on \(k\)?Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsChoose the correct conclusion about the nature of the roots of \(x^2-2\sqrt{5}x+6=0\).Class 10Quadratic EquationsNature of RootsLevel 37ExpertMathematicsWhat is the nature of the roots of the equation \(4x^2-4\sqrt{3}x+3=0\)?Class 10Quadratic EquationsNature of RootsLevel 37Expert

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